
Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this lesson?
Students will summarize data to construct a conditional relative frequency table.
Students will recognize associations between the categorical data.

Prior Knowledge: What prior knowledge should students have for this lesson?
The student can construct a twoway frequency table. The student understands and can interpret joint/marginal frequency and relative joint/marginal frequency.
The student understands ratios and converting ratios to percents.
The student understands how to interpret scales (e.g., all the numbers are in thousands).
MAFS.8.SP.1.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Guiding Questions: What are the guiding questions for this lesson?
Is there an association between gender/race and drop out rate?

Teaching Phase: How will the teacher present the concept or skill to students?
The teacher should post the vocabulary listed on the Drop Out_Handout (see attached). Have the students work in groups to develop definitions for the following: categorical variables, relative frequency, conditional relative frequency, and association. The teacher may distribute the Drop Out_Handout worksheet during this time. In a whole group setting, each group may offer their descriptions of the vocabulary in order to develop a definition that may be recorded on the handout. The teacher should direct this discussion to develop complete and concise definitions for each word (see Section I of the Drop Out_Handout_Answer Key attached).
The teacher will begin the activity by pointing out the data on the Drop Out_Handout related to male and female dropout rates in the United States from 2012. (Data is also available at http://nces.ed.gov/programs/digest/d13/tables/dt13_219.71.asp and is included as a separate attachment). Ask the students the guided question and discuss how a frequency table might be useful in answering it. Students may be asked to respond to the question and to provide reasoning to support their answer to increase interest in the data under investigation. The teacher may ask why statisticians might be interested in determining whether or not an association exists between gender and dropout rate.
The teacher may need to activate prior knowledge by reviewing concepts such as joint and marginal frequency. Students should have a clear understanding of bivariate data. Have the students identify the categorical variables in this discussion and be sure the students understand why the variables are qualitative.
Have the students complete the joint frequency table (Section II of the Drop Out_Handout attached). The teacher will ask the students, based on the information given (e.g., the number of dropouts and total population), what is needed to create the frequency table? (the number of students who stay in school, which can be found by subtracting the number of drop outs from total). Have the students answer questions on their worksheet regarding the data. Responses may also be discussed in a whole group setting.
The teacher will ask the students if in determining whether a male student or female student is more likely to drop out of school in 2012, would he or she consider males who drop out out of the total number of dropouts or males who drop out out of the total number males? If needed have the students calculate both relative frequencies and discuss how to interpret each (e.g. Male dropouts out of total dropouts would not tell us the percentage of male students that drop out, but how many of the total number of dropouts are male. This comparison could be misleading because there are more male than female students in 2012).
Next, the teacher will explain that conditional relative frequency compares the frequency count to a marginal total that represents the condition of interest. Conditional relative frequencies are used to determine whether or not there is a possible association between two categorical variables. The class will continue to discuss what these two different results would suggest about the data (e.g., if more men or women dropped out of school in 2012, or what percentage of male students or female students drop out). The teacher should ensure that the conversation includes both conditionals (i.e., row and column conditionals). Students should agree (after discussion) that to determine whether or not there was an association between gender and academic status in 2012, one should find the relative frequencies of the number of dropouts based on gender.
The teacher should direct the students to Section III of the Drop Out_Handout (attached). Students should calculate row conditional relative frequencies (e.g., male dropouts out of total male students; enrolled male students out of total male students, female dropouts out of total female students, enrolled female students out of total female students, total dropouts out of total student, total enrolled out of total students).
Students should revisit the initial (statistical) question, "Is there an association between gender and dropping out of school?"
To check for understanding, students should be able to answer the question "How can we determine associations between categorical variables?"
The teacher should move to the Guided Practice section of this lesson.
After completing the Guided Practice section, the teacher should move to the Independent Practice section of this lesson.
Suggested questions to use throughout the lesson to assess student understanding:
 What is the benefit of using a conditional relative frequency table instead of a joint or relative frequency table?
 What can conditional relative frequency tables tell us about categorical data?
 How can we determine associations between categorical variables?
 What, if anything, was surprising about the results you found?

Guided Practice: What activities or exercises will the students complete with teacher guidance?
Next, students will work on identifying associations between race and dropout rates in pairs (Section IV of the Drop Out_Handout attached). The teacher may want to facilitate a discussion around the following two questions: (This can also be done after the Guided Practice section on the worksheet.) "What is the benefit of using a conditional relative frequency table instead of a joint or relative frequency table? What can conditional relative frequency tables tell us about categorical data?"
Students will use the handout provide to examine the data of White, Black, and Hispanic dropouts.
Students will be asked to first construct a twoway relative frequency table representing the data, and then a conditional frequency table.
Students may note that the numbers of each race (for population and dropouts) do not add up to the total population and dropouts. Ask students why that might be the case (there are other races not included) and what they should put in the total column (add up the three categories given).
The teacher should monitor student responses. Students should be calculating the relative frequency by dividing the joint frequency by the marginal total for that race.
Students will be given time to construct their frequency table and will then answer questions about their findings on a handout. After this, the teacher will facilitate a review of this section with the wholeclass. If the discussion about the suggested questions did not occur during the Teaching Phase, the teacher should now ask the students the following questions:
 What is the benefit of using a conditional relative frequency table instead of a joint or relative frequency table?
 What can conditional relative frequency tables tell us about categorical data?
 How can we determine associations between categorical variables?
 What, if anything, was surprising about the results you found?

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?
Students will be given the chance to investigate the relationship of their choosing (Section V of the Drop Out_Handout attached). On their handout, they will be provided the number of dropouts and total population for Black, Hispanic, and White male and female students. They are to choose two categorical variables (i.e., a gender and a race) to see if there is an association between the variables they choose. They should write a statistical question to direct their work.
Instead of answering specific questions about their findings, they will write a paragraph answering their statistical question, explaining their conclusions, and their thoughts regarding whether or not an association was observed.

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
Students will write a reflection paragraph on what they learned in this lesson about the use of conditional relative frequency tables to investigate possible associations between categorical variables. Students should also address the question of how their table could have been constructed to present a particular bias or to reflect an association that may not actually exist.

Summative Assessment
The students will complete the Summative Assessment (see attached).

Formative Assessment
The teacher will listen to student conversations and observe student responses regarding the introductory vocabulary to assess student's recall of twoway frequency tables (See Section I of Drop Out_Handout attached). The teacher may need to review the purpose and structure of a twoway frequency table. The teacher should determine at this time if there are students who might need the Drop Out_Handout_Accommodated worksheet on which the structure of the twoway frequency table is provided.
The teacher should use Section II and III of the Drop Out_Handout (attached) to assess students' recall of the structure and purpose of a twoway frequency table. The teacher should make note at this time of any students with misconceptions and gaps that he or she could address during the Guided and Independent section of the lesson.

Feedback to Students
Feedback will be given to students during the first three sections of the Drop Out_Handout (attached) used during the lesson. The teacher will provide feedback to the students as they offer descriptions of the introductory vocabulary as he or she builds on their understanding to help them develop complete and concise definitions.